Slide rule



Aug. 17, 1926.y

R. UHLICH 2 Sheets-Sheet l Fig. 2..

R. UHLICH Aug. 17 1926.

SLIDE RULE Flg.

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PATENT OFFICE.

RUDOLF UHLICH, 0F LEIPZIG-PLAGWITZ, GERMANY.

SLIDE RULE.

Application filed November 17, 1924, Serial No. 750,246, and in Germany February 25, 1924.

My invention relates to slide? rules, and it` has particular relation to the provision ol a rule whereupon all values can be directly read irrespective of the position ot the sliding element..

ln logarithmic slide rules of the type usually employed, the gladual'ions are arranged so that one logarithmic unit is positioned on the lower body scale, and a corresponding length of one unit is positioned on the lower slide rule, while upper body and slide scales carry two logarithmic units, these latter units being equal in length. 'ith such rules there is a distinct inconvenience present. in that in some positions of the slide it is impossible to ascertain directly all oli the numerical values which it may be necessary to read. ln other words, for one portion ot' the numerical values, which portion becomes greater the further out the slide is pulled, a reverse adjustment ot' the slide is necessary. Moreover, when two logarithmic units are disposed side by side, as is the usual case in rules now employed, a small scale must be used at the expense of accuracy.

Finally, the use of reciprocal graduations makes the reading of the values ditlicult since it is necessary to consider them in an inverse direction, and under these circumstances only one calculation can be made tor each position of the slide.

My invention, therefore, has for its oh- ]'eet the provision o a slide rule so marked that at all positions of the slide, within predetermined limits, all numerical values can be read directly. Moreover, percentage rates and rates of proportion may be read directly according to their absolute Value. a

My invention will be better understood in all its aspects by reference to the accompanying drawings, in which Figure 1 is a plan view ot a slide rule embodying my invention, the scales et said rule being the simplest which may be emplayed;

Fig. 2 is a view of the rule shown in Fig. 1, with the slide pulled out to its maximum open position;

Fig. 3 is a plan view of a rule embodyingr my invention whereupon percentage values have been placed;

Fig. 4 is a view ot the rule shown in Fig. :5 with the slide pulled to the left;

Fig. 5 is a sectional View taken across the rule on the line m-m; and

Fig. (5 is a plan View ot' one end of my rule showing certain limiting stops utilized therein.

lt' will be noted, of course, that the rules shown in Figs. l to 4 inclusive, are intentionally distorted in order to illustrate more clearly the principles embodied therein. .lteierring to Fig. l, a rule is shown wherein the upper and lower body scales are designated A, and A2, while the upper and lower slide scales are designated as B, and lig, it being understood that all of the gradnations shownare of the same scale, so that either the upper or lower graduations may be used il' desired.

'l`he `graduations on the upper -hody and slide scales extend from 3 to 1 to 3, while the graduations on the lower slide and body scales extend from l to 1, these latter graduations being drawn to the same scale as those on the upper body and slide scales. It will be observed, therefore, that the upper logarithmic scale has been displaced three units to the left, while the lower scale remains as those with which we are now more or less familiar.

In order to be aule to read all the results at every position of the slide Z within such limit-s as to allow all combinations, it is necessary that a full graduation l to l() of the body scale always register with a full graduation 1 to 'l0 of the slide scale.

The limits of the extreme positions of the` slide, and it is in this predetermination that.

my rule presents novel eharmfteristies, are arrived at as follows: lVhen the slideis pulled to the lelt the division line l ol" the graduation 1), must register with the lel'thand ligure 3 on the scale A1, and when the slide is pulled to the right, the division line. fit-graduation B, must register with the ligure 3 of the graduation A1. lAs above pointed out, in order to fulfill the require4 ments within required limitation, one full logarithmic division of the body portion of the rule always registers with one full logarithmic division of the slide, and, therefore, the scales A1 and B1 are, as noted, displaced to theleft in such manner that the yvalues of the graduations on A1 and B1 are always equal to three times the value ot the graduations of A2 and B2. For example, in Fig. l the line m-m passes through the following graduations: on scale A1 the ligure 9; on scale B1 the figure 9; on scale A2 the figure 3; and on scale B2 the ligure 3, thus satisfying the above requirement.

In order to further facilitate the use of my rule the graduation A2 is lcngthcned to the left to accommodate a further subdivision or graduation section 9 to 1, designated n in Fig. l. However, even in this extreme left position, and considering the added division n, the above requirement as to equivalents is fulfilled; that is, on the body graduations z-ZJ-c-(Z-c-a equals one logarithmic division which is also equal' to f-g-t-z' on the slide, as shown in Fig. 2.

It is ot course understood that the graduations which are described in the above discussion as being at the top may be arranged below, and those which have been described as being at the bottom may be disposed at the top of the body-and slide.

A further advantage incident to the use of a scale divided in accordance with my invention is realized when it is desired to calculate percentage or proportional relation, since with a rule divided as I have just described, and provided with percentage units, calculations can be carried out without any reverse readings or preliminary calculations being required. With this latter'object in view, I provide further graduations on a scale constructed in accordance with my invention as shown in Figs. 3 and 4.

Referring to Fig. 8, the main logarithmic graduations are the same as those heretofore described in connection with Fig. l. However, on the upper body portion and above the scale A1, I have arranged a scale indicated as y%, the units of this latter scale being displaced in the same order as are the units of the original scale A1. In other words, the first two units of the logarithmic percentage table, it being remembered that this percentage table is inversely arranged with respect to the upper body scale, are positioned to the right and over the units l to 3 of the upper body scale; that is, 0% and 90% are over the ligure l on the upper body scale.

On the slide, a scale indicated as 10% is arranged over the slide scale B2. Inasmuch as thc main scales A, and B2 may be utilized for subdivisions of the percentage scales just discussed, I have further marked these scales scales x70, yC/0, the corresponding percentage for all dil'erent relations between A and B being indicated numerically on scales 772% and 2%.

The following calculations may be carried out on my scale:

(l0) Z) (1.25% (b on A, a on B).

It' the percentage is given the mark l, or l is adjusted under the corresponding value and the corresponding values for a and b. are read on the graduations A and B.

It' a and b are known, a is adjusted on scale A and Z) on scale B, the one under the other and on the corresponding separate graduation, the different per cent relations and values can be read, without variations of the position ofthe slide.

In order to more clearly explain the manner in which my novel slide rule is employed, I will hereafter set forth a plurality of examples and describ-e in detail the manner in which, given a certain set of facts, said problems may be solved.

Beginning, or instance, with a simple problem in niultiplication, we will assume that 55 is to be multiplied by 80 ;-to make this calculation, place the l in the circle appearing on scale B1 under 55 on the scale A1. 'If we now place the finder line over 8 on the scale B1, we will read thereabove on scale A1 the result Ll-l, or, of course, adding the required zeros we have 4400.

If, however, we wish to multiply 5.5 by 4, it will be noticed that it is necessary to shift the inner scales to make such a calculation, that is, it would ordinarily be required to make such a shift, but by referring to the lower scales B2, A1of my rule, the calculation can be made directly without moving the slide member, thus illustrating that any calculation may be made with one setting of the l in a circle of a certain number. For instance, to obtain the above result with the 1 still remaining With these scales so.

.under 5.5, We place the finder line over 4 [be gone through with in order to perform a division. That is, if we wish to divide 88 by 22 we place the figure 22 on scale B1 directly under 88 on scale A1, and read the result on scale A1 directly over the 1 in a circle.

In the sam-e manner we may obtain any division, even though the result does not lie on the upper scales, by reverting to the lower scales.

le may, 0f course, also perform number of successive multiplications and divisions with one setting of the scale. If, for instance, we wish to divide T() by 2O and multiply the result by 8, we proceed as follows:

Place 2 on the scale B1 under 7 ou the scale A1 and we would normally read the result of this division as 3.5 on scale A1 over the 1 in the circle on B1. But it is not necesany sary to make this partial computation; we

can immediately proceed to ligure h' ou scale B2 and directly thereunder we read the result 28 on scale A2, tl e combined division and multiplication having been performed in the latter manner.

In much the same manner we may perform problems in proportion. `For iusanee, let us fix any definite proportion, such as 5:8:15:x:40:x, etc. To obtain the unknown quantity we simply place the figure S on scale B1 under the figure 5 on scale A1; with this one setting we may obtain any set of proportional figures, such as finding 24 under 15, (Si under 40, etc.

If, however, we wish to find the proportion of figures, the upper number ot' which does not appear on scale A1, within the range covered by scale B1, we simply revert to the lower scales and read the result. For instance, 40 on scale B2 lies over 25 on scale A1, and since the problem is one of proportion, the latter two figures are, of course, reversed. By this latter method the calculation may be made. without the necessity of operating the sliding member.

If it is desired to perform problems involving the use of percentages, the red scales on the rule are made use of. If, for instance, it is desired to calculate the net price when the listprice and a certain discount per* centage is given the problem is solved as follows:

If the list price is 50 and 20% discount is offered place the 1 in the circle on scale B1 under the red 20 of the scale y% and read the net price 40 on scale A1 over the gross price 50 on scale B1. It will thus be seen that the subtraction of the discount amount is directly made in my slide rule Without the necessity of making this calculation by first finding the discount and then subtracting With the slide in the sam;` position, we can, of course, obtain the net price with any given list or gross price, by simply shifting the finder line as required. i

If, however, we wish to obtain the net' price, when we know the original price, and an additional percentage on that price must be added thereto, the probl-em must be solved as follows:

Assume, for instance, that we wish to find directly the selling price when the cest price is T0 and the increase is to be 50% et' the. cost price. To perform this calculation we place the niark 1 on the scale A2, that is,

the 1 in the triangle under the red 50 of the scale :0% and then read directly the selling price 105 on scale B1 under 70 on scale A1; it being noticed that here again the'5 calculation annot be made on the two lower seal-es, but that no change of the slide is required, the result being readable directly on the upper scale. So far as the lower` scale is concerned it will be seen that 150% of 2 is 3 or that 3 appears above 2 on the two lower scales.

. ,In Figs. 5 and G I have illustrated the 'manner in which the movement and adjust* ment vof the slide vwithin' predetermined 95 limits 1s insured. A ygroove r iseut along the middle yaxls of the lower surface of the body S and into this groove projects `a pin t, which latter pin is fixed to the lower surface of the slide Z. Cross-pins u are positioned at the ends of the aforesaid groove and limit the displacement of the slide in a direction longitudinal of the rule. The position of the aforesaid cross-pins is selected in such manner that when the slide is pulled out to the` left, or to the right, the ligure 1 on scale B1 registers on scale A1. The

with the division line o effect of ysuch limited displacement is to insure that the slide moves within such space that every full division 1 to l0 on the slide comes into registration with every full division l to 10 on the body, whereupon at every position of theslide .all results can be directly read. 110

While I'have described but two examples of rules embodying the novel features of my invention it is obvious that those skilled in the art may employ said features in other relations without departing from the spirit of my invention, and I desire, therefore, that the same be limited only by the scope of the appended claims or by the prior art.

Having described my invention what I claim as new and desire to secure by Letters Patent of the United States is 1. In a slide rule, upper and lower body portions having scales thereupon, a slide adapted yto move between said body portions, upper and lower sca-les on said slide,

the upper body and slide scales extending from the left end thereof in order as 3, 4, 5, 6, 7, 8, 9, 1, 2, 3, the lower slide and body scales extending in like manner as 1, 2, 3, 4, 5, 6, 7 8, 9, 1, or inversely, and the upper body and slide scale figures being so disposed that their 'value always amounts to three times the value of the lower .slideI and body scale figure normally thereunder.

2. In a slide rule, upper and lower body portions having scales thereupon, a slide adapted to move between said body portions, upper and lower scales on said slide, the upper body and slide seal-es extendingr from the left end thereof in order as 3, l1, 5, (3, 7, 8, 9, 1, 2, 3, the lower slide and body scales extending in like manner as 1, 2, 8, 4, 5, 6, 7, 8, 9, l, or inversely, the upper body and slide scale figure being so disposed that their value always amounts to three times the value of the lower slide and body scale figures normally thereunder, and the lower body scale being extended to the left and beyond the uppertbodygraduations in a section 9 to 1.

3. A slide rule as defined in claim 1 having a scale 0%-900% arranged over the lower slide scale in such manner that the sub-divisions of saidlower slide scale may be used as percentage graduatons between the main figures of said W70-900% scale, and having another percentage scale C75-90% reciprocally positioned over the corresponding figures ot the upper body scale, said upper Y body scale sub-divisions serving as subgraduations for the associated percentage scale.

In witness whereof, I have hereunto subscribed my name.

RUDOLF UItHJICH. Y 

